Canonical data-reconstructions via kernels, Hilbert space-valued Gaussian processes, and quantum states

Palle E. T Jorgensen; James Tian

doi:10.48550/arxiv.2405.02796

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Canonical data-reconstructions via kernels, Hilbert space-valued Gaussian processes, and quantum states

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Canonical data-reconstructions via kernels, Hilbert space-valued Gaussian processes, and quantum states

Palle E. T Jorgensen and James Tian

ArXiv.org

Cornell University

05/04/2024

DOI: 10.48550/arxiv.2405.02796

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Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We offer new results and new directions in the study of operator-valued kernels and their factorizations. Our approach provides both more explicit realizations and new results, as well as new applications. These include: (i) an explicit covariance analysis for Hilbert space-valued Gaussian processes, (ii) optimization results for quantum gates (from quantum information), (iii) new results for positive operator-valued measures (POVMs), and (iv) a new approach/result in inverse problems for quantum measurements.

Mathematics - Functional Analysis

Physics - Quantum Physics

Details

Title: Subtitle: Canonical data-reconstructions via kernels, Hilbert space-valued Gaussian processes, and quantum states
Creators: Palle E. T Jorgensen
James Tian
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2405.02796
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 05/04/2024
Academic Unit: Mathematics
Record Identifier: 9984622933902771

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